Conjugation in Representations of the Zassenhaus Algebra |
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Authors: | Bin Shu |
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Affiliation: | (1) Institute of Applied Mathematics & Physics, Shanghai Maritime University, Shanghai 200135, P. R. China, E-mail: bshu@shmtu.edu.cn, CN |
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Abstract: | Let F be an algebracially closed field of characteristic p > 2, and L be the p n -dimensional Zassenhaus algebra with the maximal invariant subalgebra L 0 and the standard filtration {L i }| pn−2 i =−1. Then the number of isomorphism classes of simple L-modules is equal to that of simple L 0-modules, corresponding to an arbitrary character of L except when its height is biggest. As to the number corresponding to the exception there was an earlier result saying that it is not bigger than p n . Received May 10, 1999, Accepted December 8, 1999 |
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Keywords: | Zassenhaus algebras (Cartan-type Lie algebras) Simple modules of Lie algebras and their isomorphism classes |
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